Between state-of-the-art mirrorless cameras and cropped-sensor DSLRs, image quality is now close enough that you would not notice the difference until your make some largish prints.
Since you mention safari which generally requires long focal-lengths, it would be a big advantage if your went with a camera with a smaller sensor. The Olympus OM-D E-M5 delivers excellent image quality with a Four-Thirds sensor which gives you a focal-length-multiplier (FLM) of 2X.
This will let you use smaller lenses to get the same reach. The E-M5 also focuses fast enough and shoots at 9 FPS which makes it very competitive with similar priced DSLRs. It is also weather-sealed with the use of a weather-sealed lens for use in adverse conditions. The smaller PEN E-PL5 is not weather-sealed but expected to produce even better image quality due to its lack of anti-alias filter in a more compact and affordable body.
The NEX series use the same sensor-size as a D5100, so while the body is smaller, once you include a long lens, the size saving greatly diminishes. This is already 18 months old but I wrote a blog post showing the size-advantage of Micro Four-Thirds lenses. The lenses shown give an equivalent reach of 600mm, which requires a 400mm on a D5100 or NEX.
So, to answer your question, you can get slightly better image quality with a DSLR at this time but it will cost you significantly in size.